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A lo largo de este trabajo construiremos estos números con detenimiento. Comenzando por el primer capítulo, en el que generalizaremos la definición de valor absoluto a cualquier cuerpo, haciendo especial hincapié en los valores absolutos no arquimedianos cuya propiedad especial dará pie a una topología métrica muy distinta a la que acostumbramos en R. También presentaremos el Teorema de Ostrowski, y daremos pequeña introducción a las valoraciones sobre un cuerpo. Tras este primer capítulo más general abordaremos la compleción de Q, presentando el problema de incompletitud de este cuerpo y construiremos un nuevo cuerpo que lo complete, definiendo así los números p-ádicos. En el tercer y último capítulo, describiremos la estructura algebraica y topológica del nuevo cuerpo Qp, daremos una idea de cómo representar sus elementos y finalizaremos el trabajo enunciando y demostrando, en dos versiones diferentes, el Lema de Hensel., Departamento de Álgebra, Análisis Matemático, Geometría y Topología, Grado en Matemáticas

The extensive use of HPC infrastructures and frameworks for running data-intensive applications has led to a growing interest in data partitioning techniques and strategies. In fact, application performance can be heavily affected by how data are partitioned, which in turn depends on the selected size for data blocks, i.e. the block size. Therefore, finding an effective partitioning, i.e. a suitable block size, is a key strategy to speed-up parallel data-intensive applications and increase scalability. This paper describes a methodology, namely BLEST-ML (BLock size ESTimation through Machine Learning), for block size estimation that relies on supervised machine learning techniques. The proposed methodology was evaluated by designing an implementation tailored to dislib, a distributed computing library highly focused on machine learning algorithms built on top of the PyCOMPSs framework. We assessed the effectiveness of the provided implementation through an extensive experimental evaluation considering different algorithms from dislib, datasets, and infrastructures, including the MareNostrum 4 supercomputer. The results we obtained show the ability of BLEST-ML to efficiently determine a suitable way to split a given dataset, thus providing a proof of its applicability to enable the efficient execution of data-parallel applications in high performance environments., This work has been partially supported by the European Commission through the Horizon 2020 Research and Innovation program and the EuroHPC JU under contract 955558 (eFlows4HPC project) and by MCIN/AEI/10.13039/501100011033 and the European Union NextGenerationEU/PRTR (PCI2021‑121957 and CEX2021‑ 001148‑S) and by the Spanish Government (PID2019‑107255GB), and Generalitat de Catalunya (contract 2021‑SGR‑00412). We also acknowledge financial support from “National Centre for HPC, Big Data and Quantum Computing”, CN00000013 ‑ CUP H23C22000360005, and from “FAIR ‑ Future Artificial Intelligence Research” project ‑ CUP H23C22000860006., Peer Reviewed, Postprint (published version)

The AI-SPRINT project, launched in 2021 and funded by the European Commission, focuses on the development and implementation of AI applications across the computing continuum. This continuum ensures the coherent integration of computational resources and services from centralized data centers to edge devices, facilitating efficient and adaptive computation and application delivery. AI-SPRINT has achieved significant scientific advances, including streamlined processes, improved efficiency, and the ability to operate in real time, as evidenced by three practical use cases. This paper provides an in-depth examination of these applications – Personalized Healthcare, Maintenance and Inspection, and Farming 4.0 – highlighting their practical implementation and the objectives achieved with the integration of AI-SPRINT technologies. We analyze how the proposed toolchain effectively addresses a range of challenges and refines processes, discussing its relevance and impact in multiple domains . After a comprehensive overview of the main AI-SPRINT tools used in these scenarios, the paper summarizes of the findings and key lessons learned., Peer Reviewed, Postprint (published version)

After large-magnitude earthquakes, a crucial task for impact assessment is to rapidly and accurately estimate the ground shaking in the affected region. To satisfy real-time constraints, intensity measures are traditionally evaluated with empirical Ground Motion Models that can drastically limit the accuracy of the estimated values. As an alternative, here we present Machine Learning strategies trained on physics-based simulations that require similar evaluation times. We trained and validated the proposed Machine Learning-based Estimator for ground shaking maps with one of the largest existing datasets (<100M simulated seismograms) from CyberShake developed by the Southern California Earthquake Center covering the Los Angeles basin. For a well-tailored synthetic database, our predictions outperform empirical Ground Motion Models provided that the events considered are compatible with the training data. Using the proposed strategy we show significant error reductions not only for synthetic, but also for five real historical earthquakes, relative to empirical Ground Motion Models., This work has been funded by the European Commission’s Horizon 2020 Framework program and the European High-Performance Computing Joint Undertaking (JU) under grant agreement No 955558 and by MCIN/AEI/ 10.13039/501100011033 and the European Union NextGeneration EU/PRTR(PCI2021-121957), project eFlows4HPC. This research has been supported by the European High-Performance Computing Joint Undertaking (JU) as well as Spain, Italy, Iceland, Germany, Norway, France, Finland, and Croatia under grant agreement no. 101093038, (ChEESE-CoE). The authors acknowledge the Center for Advanced Research Computing (CARC) at the University of Southern California for providing computing resources that have contributed to the research results reported within this publication. URL: https://carc.usc.edu. This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725, and the National Center for Supercomputer Applications under the Blue Waters Sustained-Petascale Computing Project. SCEC is funded by USGS Cooperative Agreement G17AC00047 and NSF Cooperative Agreement EAR1600087., Peer Reviewed, Postprint (published version)

In the last years, there has been a significant increment in the quantity of data available and computational resources. This leads scientific and industry communities to pursue more accurate and efficient Machine Learning (ML) models. Random Forest is a well-known algorithm in the ML field due to the good results obtained in a wide range of problems. Our objective is to create a parallel version of the algorithm that can generate a model using data distributed across different processors that computationally scales on available resources. This paper presents two novel proposals for this algorithm with a data-parallel approach. The first version is implemented using the PyCOMPSs framework and its failure management mechanism, while the second variant uses the new PyCOMPSs nesting paradigm where the parallel tasks can generate other tasks within them. Both approaches are compared between them and against MLlib Apache Spark Random Forest with strong and weak scaling tests. Our findings indicate that while the MLlib implementation is faster when executed in a small number of nodes, the scalability of both new variants is superior. We conclude that the proposed data-parallel approaches to the Random Forest algorithm can effectively generate accurate and efficient models in a distributed computing environment and offer improved scalability over existing methods., This work has been supported by the Spanish Government (PID2019-107255GB) and by the MCIN/AEI /10.13039/501100011033 (CEX2021- 001148-S), by the Departament de Recerca i Universitats de la Generalitat de Catalunya to the Research Group MPiEDist (2021 SGR 00412), and by the European Commission’s Horizon 2020 Framework program and the European High-Performance Computing Joint Undertaking (JU) under grant agreement No 955558 and by MCIN/AEI/10.13039/501100011033 and the European Union NextGenerationEU/PRTR (PCI2021-121957, project eFlows4HPC), and by the European Commission through the Horizon Europe Research and Innovation program under Grant Agreement No. 101016577 (AI-Sprint project)., Peer Reviewed, Postprint (author's final draft)

Recent research has shown the possibility to achieve microconfined turbulence utilizing supercritical fluids under high-pressure transcritical conditions. This has generated increasing interest in the hybrid nature of the fluid thermophysical properties near the pseudo-boiling region. However, obtaining thermophysical experimental data of microfluidic transcritical systems is challenging due to the difficulties associated with high-pressure experiments, and the focus on velocity-related data acquisition of traditional experimental techniques, such as particle image velocimetry and particle tracking velocimetry. To overcome these challenges, this work introduces a novel framework based on a physics-constrained neural network to recover thermophysical information from velocity data at high-pressure turbulent transcritical conditions. By incorporating thermophysical constraints and boundary conditions into the network architecture and the loss function, the proposed model surpasses non-physically informed approaches in terms of accuracy, satisfaction of thermophysical constraints and preservation of bulk quantities., This work is funded by the European Union (ERC, SCRAMBLE, 101040379)., Peer Reviewed, Postprint (published version)

Recent research has highlighted the potential of supercritical fluids under high-pressure transcritical conditions to achieve microconfined turbulence as a result of the thermophysical properties they exhibit in the vicinity of the pseudo-boiling region. This has led to increased interest in understanding their hybrid thermophysical properties when operating near the pseudo-boiling transitioning region. However, despite the potential benefits of microfluidic systems working under transcritical conditions, limited experimental data is available due to the inherent challenges of performing experiments at high-pressure conditions. In addition, traditional experimental methods, such as particle image velocimetry and particle tracking velocimetry, are inadequate for measuring thermophysical properties under such conditions, since they are primarily designed for velocity-related data acquisition. In this regard, this work introduces an efficient thermodynamics-informed neural network framework for reconstructing thermophysical information from velocity data in high-pressure turbulent transcritical regimes. The proposed model incorporates thermophysical constraints through a thermodynamics-informed loss function consisting of the residual of the real-gas equation of state and integrates boundary conditions into the network’s architecture to ensure their satisfaction. The performance of the proposed framework is evaluated through the analysis of two test cases and compared against non-physically informed models. The results demonstrate the superior accuracy, robustness, and satisfaction of physical constraints achieved by the proposed model, as well as its ability to reconstruct averaged thermophysical profiles and preserve bulk quantities with a relative error reduction of approximately 2×. In addition, the physically-consistent predictions provided by the model enable a more accurate reconstruction of dependent thermophysical properties., The authors gratefully acknowledge the Formació de Professorat Universitari scholarship (FPU-UPC 2022) of the Universitat Politècnica de Catalunya BarcelonaTech (UPC) (Spain), the SRG program (2021-SGR-01045) of the Generalitat de Catalunya (Spain), the Beatriz Galindo program (Distinguished Researcher, BGP18/00026) of the Ministerio de Educación Formación Profesional (Spain), and the computer resources at FinisTerrae III & MareNostrum and the technical support provided by CESGA & Barcelona Supercomputing Center (RES-IM-2023-1-0005, RES-IM-2023-2-0005). This work is funded by the European Union (ERC, SCRAMBLE, 101040379)., Peer Reviewed, Postprint (published version)